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Swinburne University of Technology Sarawak Campus

The wonders of mechanical advantage

April 18, 2012

By Dr Manas Kumar Haldar

It was late morning. Six-year-old Johnny was playing around the house. “Mom”, he said, “You always lift me up. I want to lift you up too”. “When you get older, you will be strong enough,” said his mother Annie. “But I can lift you up now,” said Johnny. He took Annie to the seesaw in the playground and asked her to sit on it close to the support at the centre of the seesaw. Then he sat on the other side of the seesaw further away from the support than Annie. With a bit of trial and error in his position, little 15kg Johnny managed to lift her 60kg mother up at the other end of the seesaw.

You might have come across such a scene in the park but have you ever wondered how this is possible? In the above example, the seesaw multiplied Johnny’s force of weight of 15kg by a factor of 4. This is the mechanical advantage provided by the seesaw, which represents what is known in physics as a lever of the first kind. In this type of lever, the support called fulcrum, lies between the force (Johnny’s weight) and the load (Annie’s weight).

The operation of a seesaw can be explained by principles of mechanics, a branch of physics. This may be a bit difficult for some. So let me explain the operation with what was called the law of the lever by the famous scientist and mathematician, Archimedes, in 250BC. The force on a load on a lever is the applied force times the distance of the applied force from the support divided by the distance of the load from the support, when everything is motionless. The lever multiplies your force, by the ratio of the distances and this ratio is the mechanical advantage.

The distance from the support to Johnny must have been at least four times the distance of his mother from the support. What happens when Johnny sits further away from the support? It is harder to explain because Johnny’s side of the seesaw will then hit the ground which produces an upward force of reaction. But the mechanical advantage remains the same.

There are other mechanical systems which provide mechanical advantage. Take for example, a nut cracker. The end of the nutcracker is fixed, so it is the support or fulcrum. The nut in the middle is the load. You apply the force on the arms of the nutcracker. The force on the nut is higher than the force you apply. So the nutcracker again gives you a mechanical advantage. Unlike in the seesaw, the load lies between the force and fulcrum. This is called a lever of the second kind.

A wheelbarrow follows the same principle. The support is the wheel at one end and the force is applied at the other end to lift the load in between the two.  The law of the lever can be applied. The force on the load is greater than the applied force by the ratio of distances.

For the first lever mentioned above, the support is between the force and the load. For the lever of the second kind, the load is between the support and the force. There is a third kind of lever where the force is between the support and the load.

Mechanical advantage is not restricted to levers. Think of stopping a car by stepping on the brake pedal. But the car brake is more than just a lever. It is a combination of a hydraulic system and a lever. The total mechanical advantage is the product of the mechanical advantages of the two. So you need to put in much less force than what would be necessary to press the brake shoes against the rotating wheels. Indeed without mechanical advantage, it will be difficult for us to perform many tasks in life.  

Dr Manas Kumar Haldar is an associate professor with the School of Engineering, Computing and Science at Swinburne University of Technology Sarawak Campus. He can be contacted at mhaldar@swinburne.edu.my